In multi-carrier systems, e.g., OFDM systems, channel estimation schemes are used for coherent detection of a received signal. OFDM is based on the modulation technique of frequency division multiplexing (FDM). The OFDM technique differs from traditional FDM by having subcarriers, which are orthogonal to each other. The modulation technique used in an OFDM system helps to overcome the effects of a frequency selective channel. A frequency selective channel occurs when the transmitted signal experiences a multipath environment.
The goal of channel estimation is to estimate the time-varying channel frequency response for each OFDM symbol. The channel can be estimated by using scattered reference symbols (pilot tones) in the frequency domain. Since the reference symbols are also scattered in the time-domain, it is necessary to estimate the channel in two dimensions, in the time-domain as well as in the frequency-domain. The channel can also be represented by its impulse response instead of its frequency response and the time-varying behaviour of the impulse response can be tracked. In order to track the channel frequency response, the subcarriers with reference symbols are used to find estimates of the channel for the subcarriers at OFDM symbols without reference symbols. Firstly, the channel is estimated in the frequency direction based on all subcarriers with reference symbols. Secondly, the frequency response for each OFDM symbol is found by interpolating in the time-domain between the known estimates. Alternatively, the ordering could be reversed such that time-processing is carried out in the first step and frequency processing is carried out in the second step.
Interpolation based channel estimation can be carried out in numerous ways, e.g., by simple linear interpolation between adjacent reference symbols (e.g., pilots tones) or by fitting a polynomial function (e.g., by a least-squares method) to the sampled channel transfer function. Even though channel estimation based on simple linear interpolation is computationally tractable it tends to perform badly in channels with high frequency selectivity. A more advanced approach is to apply Wiener Filtering (or Linear Minimum Mean Square Error (LMMSE)) which relies on some statistical features of the underlying channel transfer function to be estimated (see e.g., “Two-dimensional pilot-symbol-aided channel estimation by Wiener filtering”, Hoeher, P.; Kaiser, S.; Robertson, P.; Acoustics, Speech, and Signal Processing, 1997. ICASSP-97., 1997 IEEE International Conference, Volume 3, 21-24 Apr. 1997, pages 1845-1848). However, this approach tends to become computationally intractable even for moderate sized pilot sets. Also the frequency domain smoothing matrix associated to delay (transform) domain channel estimation tends to become computationally intractable to calculate or too large to store for practical purposes.
Hence, in practical implementations, in order to reduce the computational complexity of the channel estimator as well as to reduce the memory for storing pre-computed filters (see e.g., US 20050105647A1) a sliding window approach is typically adopted. However, there are limits as to how small this sliding window can be made before the performance of the channel estimator begins to degrade. This in turn means that the processing gain of the estimator is upper limited by the size of the window. Hence, in channels with large coherence bandwidth and/or large coherence time these estimators would be limited by the window size and not the characteristics of the channel.